In-plane electronic anisotropy in underdoped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ revealed by partial detwinning in a magnetic field

We present results of angle-dependent magnetoresistance measurements and direct optical images of underdoped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ which reveal partial detwinning by action of a 14 T magnetic field. The relative change in the twin domain population for the given field is modest, of order $5–15\mathrm{\%}$. The associated field-induced hysteretic changes in the resistivity are up to 5% for intermediate Co concentrations, implying a large in-plane resistivity anisotropy in the broken-symmetry state. Based on the generic anisotropic susceptibility of collinear antiferromagnets, we infer a smaller resistivity along the antiferromagnetic ordering direction. The observation of field-induced motion of twin boundaries indicates a substantial magnetoelastic coupling in this material.

Figure 1

(Color online) The in-plane magnetoresistance $\Delta {\rho }_{ab}/{\rho }_{ab}$ (%) of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ for $x=2.5\mathrm{\%}$ for two specific current orientations (samples A and B). The angle independent part of the magnetoresistance for sample B has been subtracted for clarity. The data were taken at 84 K, below both $T_s$ and $T_N$ for this cobalt concentration. The geometry of the measurement is indicated below each panel. Both current and field are in the $ab$ plane and the angle of the magnetic field is measured relative to the current direction. For sample A current is applied parallel to the orthorhombic $a/b$ axis whereas for sample B current is applied at $45°$ to the orthorhombic $a/b$ axis.

Figure 2

(Color online) The angle-dependent magnetoresistance $\left({\rho }_{ab}\left(\theta ,14T\right)-\overline{{\rho }_{ab}}\right)/\overline{{\rho }_{ab}}$ [where $\overline{{\rho }_{ab}}$ is the average of ${\rho }_{ab}\left(\theta ,14T\right)$ over $\theta$] as a function of angle and temperature of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ for (a) $x=3.6\mathrm{\%}$ and (b) $x=2.5\mathrm{\%}$. The magnitude of MR is indicated by the color scale. Vertical lines indicate $T_s$ and $T_N$, as determined for these samples by the derivative of the resistivity (shown above each panel).

Figure 3

(Color online) Representative magnetoresistance data for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of field and angle for $x=1.6\mathrm{\%}$ at $T=80\text{K}$ [panels (a) and (b)] and $T=20\text{K}$ [panels (c) and (d)]. For all cases the current is aligned parallel to orthorhombic $a/b$ axes and field is applied parallel to the $ab$ plane (i.e., sample A configuration). For field sweeps, the magnetic field was swept from 0 to 14 T, then 14 to $-14\text{T}$, then back to 0T following an initial zero-field cool. Data were taken for fields aligned parallel (red) and perpendicular (green) to the current. Angle sweeps were performed in a field of 14 T following an initial zero-field cool. Data were taken continuously as the angle was increased from $0°$ to $360°$ and then back to zero. The nonzero offset in (c) and (d) results from a slight mixing of out of plane field component due to a small sample misalignment.

Figure 4

(Color online) Time dependence of the resistivity for a representative sample with $x=1.6\mathrm{\%}$, revealing thermal relaxation of the field-induced changes in the resistivity. The sample was initially cooled to 2 K in 14 T, before the field was cycled to zero. The sample was then warmed to (a) 5 K and (b) 10 K, and the resistivity measured as a function of time after the temperature had stabilized. Data are fit by an exponential relaxation with resulting time constants of $3.3\pm 1.8\times {10}^3$ and $1.8\pm 0.4\times {10}^3\text{s}$, respectively.

Figure 5

(Color online) Temperature dependence of the resistivity for representative samples with $x=1.6\mathrm{\%}$ [panels (a) and (b)] and $x=2.5\mathrm{\%}$ [panels (c) and (d)]. Data were taken during an initial field cool (FC, solid symbols) in 14 T, after which the field was cycled to zero and the resistivity measured in zero field while warming (ZFW, thin lines). The current is aligned parallel to the $a/b$ orthorhombic axes and the field applied either parallel (red) or perpendicular (green) to the current. For comparison, data are also shown for the same samples while cooled in zero field (ZFC, black symbols). The FC MR $\left[\left({\rho }_{\text{FC}}-{\rho }_{\text{ZFC}}\right)/{\rho }_{\text{ZFC}}\right]$ and ZFW resistivity difference induced by field cooling $\left[\left({\rho }_{\text{ZFW}}-{\rho }_{\text{ZFC}}\right)/{\rho }_{\text{ZFC}}\right]$ for the two field configurations are also plotted in (b) for $x=1.6\mathrm{\%}$ and (d) for $x=2.5\mathrm{\%}$. Vertical lines indicate $T_s$ and $T_N$.

Figure 6

(Color online) Representative optical images of a $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ sample for $x=2.5\mathrm{\%}$, revealing the partial detwinning effect of an in-plane magnetic field. The images (obtained as described in the main text) were taken at $T=40\text{K}$ below both $T_s$ and $T_N$. The initial image (a) was taken in zero field, following a zero field cool from above $T_N$. The field was then swept to 10 T, at which field the second image (b) was taken. Horizontal intensity profiles, shown below each image, were calculated by integrating vertically over the image area after background subtraction and noise filtering. Boundaries between domains were estimated as described in the main text, resulting in an estimate of the relative fraction of the two domains indicated by black and white stripes below the figures. The field, which was oriented along the orthorhombic $a/b$ axes, has clearly moved the twin boundaries, favoring one set of twin domains (light) over the other (dark).